\begin{problem}{Covering Points}{cover.in}{cover.out}{2 seconds}{256 megabytes}

%Author: Andrew Lopatin
%Text Author: Andrew Lopatin
%Description: DP

Today, Vasya is sent to Research Institute of Spheres and Circles (RISC). This
institute studies all tasks dealing with spheres and circles, and now Vasya is 
asked to do something with circles too.

Given $n$ points on the plane, it is required to cover them all with exactly
$k$ circles of minimal possible equal radii. Circles are allowed
to touch or intersect each other. Could you help Vasya to do this?

\InputFile

Input consists of one or more test cases. Each case starts with the line containing two
integers $n$ and $k$ ($1\le n\le 15$, $1\le k\le n$), followed by $n$ lines, 
each describing one point
by its integer coordinates $x_i$ and $y_i$. 
Points are allowed to coincide.
All coordinates do not exceed $1000$ by
an absolute value. The input is terminated by a fake case $n=k=0$. The total
sum of all $n$ over all cases in a single input does not exceed $150$.

\OutputFile

For each case, output the minimal radius first, followed by an example of 
covering. If there are multiple solutions, any will do. Radii should be 
accurate up to at least six digits after decimal point, and points are checked to
be covered with precision $10^{-6}$ by the circles with the radius and centers you output. 
We recommend to output real numbers
as precisely as possible to prevent any
precision issues. Adhere to the sample output format shown below.

Note that a circle of zero radius is a single point.

\Examples

\begin{examplewide}
\exmp{
3 2
0 0
0 1
0 2
3 1
0 0
0 1
1 0
0 0
}{
Case 1: The minimal possible radius is 0.5
~~circle 1 at (0.0, 0.5)
~~circle 2 at (0.0, 2.0)
~
Case 2: The minimal possible radius is 0.7071067811865476
~~circle 1 at (0.5, 0.5)
}%
\end{examplewide}

\end{problem}
